The first step to this question is to decide x and y variables. Since the cost depends on the number of lessons, cost is the dependent (y) variable, and the number of lessons is the independent (x) variable. We can say that (7,82) is one point, and (11, 122) is the second point. This gives us x1 = 7, y1 = 82, x2 = 11, y2 = 122.
The next step is to find the slope (m) of the line. This is accomplished by dividing the change in y values by the change in x values. This is also called rise over run, and is calculated by (y2-y1)/(x2-x1). This gives us:
m = (122-82)/(11-7)=40/4=10. The slope of the line is 10, therefore each lesson costs 10 additional dollars.
However, the line does not necessarily cross the y axis at 0, as there might be some signup fees for the lesson.We need to determine the y-intercept, or the "b" portion of y=mx+b. To do this, we plug in one of our coordinate pairs along with the slope that we calculated:
y = mx+b
82 = 10*7+b
82 = 70+b
b = 12
So now we see that there is a $12 startup fee for these dance lessons. Our finalized equation can be written: y = 10x+12, which says that after a $12 startup cost, each lesson costs $10. To put it in terms of the question, the equation becomes C = 10L + 12.
Now we can find the cost of four lessons by plugging in 4 for L:
C = 10*4+12
C=52.
The cost for 4 lessons is $52.
Final Answers:
Linear Equation: C = 10L + 12.
Cost for 4 lessons: $52.
